Emergence of envelop solitary waves from initial localised pulses within the Ostrovsky equation
Article
Article Title | Emergence of envelop solitary waves from initial localised pulses within the Ostrovsky equation |
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Article Category | Article |
Authors | Grimshaw, R. H. J. (Author) and Stepanyants, Y. A. (Author) |
Journal Title | Radiophysics and Quantum Electronics |
Journal Citation | 63 (1), pp. 21-28 |
Number of Pages | 8 |
Year | 2020 |
Publisher | Springer |
Place of Publication | United States |
ISSN | 0033-8443 |
1573-9120 | |
Digital Object Identifier (DOI) | https://doi.org/10.1007/s11141-020-10031-1 |
Web Address (URL) | https://link.springer.com/article/10.1007/s11141-020-10031-1 |
Abstract | We study the emergence of steady wave packets in the form of envelope solitary waves (envelope solitons) which evolve from localized pulse-type initial conditions in the long-term evolution within the framework of the Ostrovsky equation. Ostrovsky equation derived in 1978 describes weakly nonlinear oceanic waves affected by the Earth’s rotation. Subsequently it became clear that this equation is universal, and is widely used for the description of waves in various settings. It is well-known that in applications to media with a negative small-scale dispersion this equation does not possess steady solitary wave solutions. In particular, the evolution of an initial Korteweg-de Vries (KdV) soliton results in the emergence of envelope solitons which can be described by the nonlinear Schr¨odinger equation (NLS) when the amplitude of the initial KdV soliton is sufficiently small. However, the derivation of the corresponding NLS still has not been sufficiently comprehensive, which resulted in contradiction with some numerical simulations. Here, we revisit this problem and suggest a new approach to the construction of the emerging envelope solitons. |
Keywords | envelop solitary waves; Ostrovsky equation; soliton; waves in rotating fluid |
ANZSRC Field of Research 2020 | 401207. Fundamental and theoretical fluid dynamics |
370803. Physical oceanography | |
490109. Theoretical and applied mechanics | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | School of Sciences |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q5z4z/emergence-of-envelop-solitary-waves-from-initial-localised-pulses-within-the-ostrovsky-equation
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